Question

Suppose f(x) = x³ - 6x + 1. Does the Intermediate Value Theorem guarantee that f(x) will have a root on the interval (2, 3)? Answer yes or no in the answer box in D2L and put your work and answer with explanation on your paper.

Answer 1

Yes (see below for explanation

Explanation:

`f(2)=2^3-6(2)+1=8-12+1=-4+1=-3\\f(3)=3^3-6(3)+1=27-18+1=9+1=10`

Therefore, since
`f(2) < 0 < f(3)`, then the Intermediate Value Theorem guarantees that
`f(x)` will have a root on the interval
`(2,3)`.